A partnership will generate revenue p = 2x + y + xy, where x and y are the efforts of partners 1 and 2, respectively. Partners bear effort costs of 2x² and 0.5y2, respectively, and they share the revenue equally. What is the ratio of the equilibrium efforts x/y? 1/2 1
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- Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose that potential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whichever stand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below. 1/4 1/2 3/4 Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location? a. One of them puts a stand at 3/4 and the other puts a stand at 1/4 b. Chad and Jason put their stands right next to each other at 1/2 c. One of them puts a stand at 0 and the other puts a stand at 1 d. There is no Nash EquilibriumFirm 1 and Firm 2 compete in the same product market by setting quantities q₁ and 92, respectively. They have the same marginal cost c₁ = C₂ = 40. The market demand is p=1240 Q, where Q = 91 +92. 19. Suppose the game is played for one period. What are the equilibrium quantities? (a) q₁ = 1000, 92 1000 (b) q₁ = 800, q2 = 800 (c) 91 = 600, q2 = 600 (d) 9₁ = 400, q2 = 400 (e) 9₁ = 200, q2 = 200 In questions 19-21, suppose that this game is repeated for infinitely many periods. Firms have the same discount rate 8. Consider the situation in which the two firms are trying to implement a collusion scheme. With this intent, they employ the following grim-trigger strategy: in the first period, each firm produces the collusion quantity; from period two onwards, the firm keep producing the collusion quantity as long as no firm has ever pro- duced any quantity other than the collusion quantity; otherwise, the firm plays the Nash Equilibrium of the stage game. As you will see, what varies from one…Three firms share a market. The demand function is P(q1, 92, 93) = 10 – q1 – 92 – 93, where q; is the output of firm i, Player i. The marginal cost per unit for each firm is zero. Suppose firm 1 is a market leader, and that firm 2, and firm 3 choose q2 and q3 simultaneously after observing q1 Find the SPE of this game. How much is produced by firm 2? Numerical answer How much is produced by firm 1, 2, and 3?
- Your firm must decide whether or not to introduce a new product. If you introduce the new product, your rival will have to decide whether or not to clone the new product. If you don’t introduce the new product, you and your rival will earn $1 million each. If you introduce the new product and your rival clones it, you will lose $5 million and your rival will earn $20 million (you have spent a lot on research and development, and your rival doesn’t have to make this investment to compete with its clone). If you introduce the new product and your rival does not clone, you will make $100 million and your rival will make $0. 1. Set up the extensive form of this game. 2. Should you introduce the new product? 3. How would your answer change if your rival has “promised” not to clone your product? 4. What would you do if patent law prevented your rival from cloning your product?A4 1. Two chemical companies, A and B, operate in a small New England town. Every week A releases 40 gallons of dioxin into the town’s aquifer, while B releases 30 gallons during the same time frame. It would cost A $800 per gallon to clean up its production, while B can clean up its waste at a cost of $500 per gallon. After this issue is raised at a town hall meeting, the town’s residents vote to reduce total dioxin pollution to 20 gallons per week. a. What would be the total cost of pollution reduction if each company were limited to 10 gallons of waste per week? b. What would the total costs be if each company received 10 gallons worth of tradable pollution credits? 2. A wheat farmer and a cattle rancher occupy adjacent parcels of land. Every year the farmer builds a fence to keep the cattle out of his field, and every year the rancher tears the fence down so that the cattle can roam free. The farmer values the wheat that gets destroyed at $300, while the rancher values having a…Exercise 6.7. Suppose two identical companies produce wood stoves and they are the only ones on the market. Its costs are given by: C1 (q1 )=200q1 and C2 (q2) = 200q2. And the inverse market demand curve is: P=2000-2Q, where Q =q1 + q2 Get the Cournot-Nash equilibrium. Calculate the profits of each company. Show graphically. Suppose that the two companies form a cartel to maximize joint profits. How many stoves will you produce? Calculate the profits of each company. Represent graphically. Managers now note that explicit agreements to collude are illegal. Each company must decide on its own whether to produce the amount of Cournot or that of the cartel.
- Two companies must collaborate to develop a new product. They must choose between two products, product A or product B. While Company ABC has a patent for product A, Company XYZ has a patent for product B. If a product gets developed, the company without a patent must pay licensing fees of $200K. The companies' profits (in $1000) are as follows: Table 2: Product Innovation ABC Product A Product B XYZ Product A Product B 300,100 0,0 1. What are the equilibria in pure strategies? 2. Which basic game does it resemble? 0,0 100,300Taylor, Faith, Jay, and Jessica are college roommates. They're trying to decide where the four of them should go for spring break: Orlando or Las Vegas. If they order the tickets by 11:00 PM on February 1, the cost will be just $500 per person. If they miss that deadline, the cost rises to $1,200 per person. The following table shows the benefit (in dollar terms) that each roommate would get from the two trips. Roommate Taylor Benefit from Orlando Benefit from Las Vegas Faith $1,250 $800 $550 $800 Jay Jessica $650 $600 $850 $1,050 The roommates tend to put off making decisions. So, when February 1 rolls around and they still haven't made a decision, they schedule a vote for 10:00 PM that night. In case of a tie, they will flip a coin between the two vacation destinations. The roommates will get the most total benefit if they choose to go to Given the individual benefits each roommate receives from the two trips, which trip will each roommate vote for? Fill in the table with each…(1) Two firms (A and B) that produce timber products pollute a local forest with pesticides used to grow trees. Currently, firm A releases 100 pounds of pesticide waste into the forest per month, while firm B releases 140 pounds of pesticide waste into forest per month. The table below shows the cost of reducing pesticide waste by increments of 10 pounds for each firm. For each firm, reductions beyond 50 pounds would be virtually impossible to accomplish and expensive if it is to stay in business, because some pesticide must be used. Total cost of reducing Firm A pesticide waste by 10 pounds 20 pounds 30 pounds 40 pounds 50 pounds Firm B $6 $4 $18 $12 $36 $24 $60 $40 $90 $64 Suppose the government wants to reduce pesticide waste level to 180 pounds. That is, the government wants to reduce pesticide waste from its current monthly level to 180 pounds per month. To achieve this goal, the government decides to issue permits to pollute. A total of 18 permits are issued, where each permit…
- Individual A Cooperate Defect Individual B Cooperate 28, 28 34,8 Defect 8, 34 12, 12 Suppose individuals live in villages that are homogeneous by type and a fractions of their interactions takes place in their village, the rest occurring in the city where the types were mixed. The fraction of the population who are cooperators is a. a) Write the expected return functions for cooperate and defect as a function of s and a. b) Under which conditions does an interior equilibrium exist for the fraction of the population playing cooperate (a) c) If the interior equilibrium for a exists, is the interior equilibrium unstable or stable? d) Find the impact of higher s on the interior equilibrium for a. What intuitively does this outcome mean? Discuss your answer.Answer all questions, show all working. Marta and Sara are two students that devote part of their free time to doing surveys for a market research company. The income obtained from this activity depends on the number of surveys they do, bearing in mind that the girls may freely choose the interviewees. As they both live in the same neighborhood in case, they just interview their neighbors (N), they compete for the same people and their monthly income is about 250 Euros. If they both choose to go to other neighborhoods of the city and interview strangers (S), they can carry out more surveys and both their incomes would be 400. If one of them decides to go and interview people in another neighborhood but the other one does not, the former will obtain income for 500, and the latter for 300, and vice versa. After receiving the order from the company, Marta is always the one who starts to work first. Sara has information about the places where Marta has done the surveys. Please:…Company A and Company B are competing oligopolists. Both companies are considering increasing or maintaining their prices The payoff matrix shows the profits of the companies in millions based on their possible actions. Company B Increase Price Maintain Price Company A Increase Price $50, $40 $35, 530 Maintain Price 555, $45 $60, $35 The government offers a $5 milon subsidy to maintain current pricing. What is the expected outcome of the new payoff matrix, given the subsidy? The Nash equilibrium changes, and both companies will maintain their prices O The Nash equilbrium changes, and both companies will increase their prices O The Nash equilibrium remains the same, and both companies will increase their prices O Company A wit increase its price, whie Company B maintains its price. O Company A will maintain its price, while Company Bincreases ts price.